Quantum and time
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Quantum Theory and the Concept of Time
Time Asymmetry in Quantum Theory
The operational formulations of quantum theory exhibit a distinct time orientation, which contrasts with the time-symmetric nature of microscopic physics. This asymmetry arises from the inherent assumptions about the users of the theory, who are typically focused on predicting future events based on past information. The primary mathematical constructs in these formulations implicitly assume knowledge of the past but not the future, leading to a perceived asymmetry between knowns and unknowns.
Quantum Theory Without Predefined Time
Traditional quantum theory relies on a predefined notion of time, posing challenges for developing a quantum theory of gravity where space-time's causal structure is dynamic and probabilistic. A novel approach proposes a generalized formulation of quantum theory that eliminates the need for predefined time or causal structure. This method uses an isomorphism between transformations and states, allowing for a time-neutral representation. In this framework, operations are associated with regions connected in networks without assumed directionality, accommodating indefinite causal order and other acausal structures.
Emergence of Time from Quantum Events
Time in quantum mechanics and general relativity are fundamentally different, with the former treating time as an independent parameter and the latter as observer-dependent and dynamic. A proposed resolution extends the classical concept of an event to the quantum domain, defining an event as an information transfer between physical systems. This perspective introduces quantum states of events with space-time-symmetric wave functions, suggesting that time emerges as an observer-dependent property from a sequence of events. This sequence creates a counterfactual asymmetry, giving rise to the flow of time as perceived by the observer.
Quantum Time and Evolution
In some models, time is represented by a quantum operator, similar to position operators in the Schrödinger representation. This operator can be described by a positive operator-valued measure (POVM), providing a quantum observable for spacetime positions. Quantum evolution in this context is a stochastic process based on Lüders' projection postulate, generalizing unitary evolution and treating time as a quantum observable in a consistent, observer-independent manner.
Quantum Eraser and Temporal Interpretation
The quantum eraser effect highlights the stark differences between classical and quantum conceptions of time. This phenomenon demonstrates how the availability or erasure of past information can influence the interpretation of present data. Various experiments, such as the entanglement quantum eraser and kaon quantum eraser, have explored these effects, underscoring the non-classical nature of time in quantum mechanics.
Entropic Dynamics and the Arrow of Time
Quantum mechanics can be derived using the method of maximum entropy, where time is introduced as a device to track change. In this entropic dynamics framework, the entropy of extra variables drives the dynamics of particles, and vice versa. This approach naturally incorporates an arrow of time, with the wavefunction's magnitude and phase providing statistical interpretations related to the distribution of particles and the entropy of extra variables, respectively.
Discrete Quantum Transitions and Time
Max Born's original version of quantum theory, "Matrix Mechanics," introduced the concept of discrete quantum transitions, replacing the classical notion of continuous time evolution. This framework suggests that time, like other physical quantities, is subject to quantum uncertainties, challenging the classical space-time concepts and emphasizing the discontinuous nature of quantum physics.
Quantum Clocks and the Problem of Time
The problem of time in quantum physics remains unresolved, hindering the development of a comprehensive theory of quantum gravity. Recent proposals advocate for considering time as an intrinsic quantum observable, alongside conventional external time. These approaches aim to reconcile the differences between relativity and quantum physics, potentially leading to a unified theory that incorporates a consistent treatment of time.
Time-Reversal Invariance in Quantum Theories
There is ongoing debate about whether deterministic and indeterministic quantum theories are time-reversal invariant. Some arguments suggest that time is inherently directional in a quantum world. However, redefining the meaning of time-reversal invariance or adopting alternative interpretations of the wave-function can restore this invariance, highlighting the complexity of time's role in quantum mechanics.
Joint States Over Time in Quantum Channels
A recent study challenges the notion that there is no physically reasonable assignment for producing a joint state on the tensor product of input and output spaces in quantum channels. By restricting the domain of this assignment to more faithfully represent the given data, it is possible to bypass previous no-go results, suggesting a nuanced understanding of the distinction between space and time in quantum settings.
Conclusion
The interplay between quantum theory and the concept of time reveals a complex and multifaceted relationship. From the asymmetry in operational formulations to the emergence of time from quantum events, and the challenges of integrating time into quantum gravity, these studies highlight the need for innovative approaches to reconcile the differences between classical and quantum perspectives on time.
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